

A293063


Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of kdimensional magnetic subperiodic groups in ndimensional space, counting enantiomorphs.


3



2, 5, 7, 31, 31, 80, 122, 394, 528, 1651, 1202
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OFFSET

0,1


COMMENTS

Magnetic groups are also known as antisymmetry groups, or blackwhite, or twocolor crystallographic groups.
T(n,0) count ndimensional magnetic crystallographic point groups, T(n,n) count ndimensional magnetic space groups. The name "subperiodic groups" is usually related to the case 0 < k < n only, i.e., magnetic groups of ndimensional objects including k independent translations which are subgroups of some ndimensional magnetic space groups.
The BohmKoptsik symbols for these groups are G_{n,k}^1, except for the case k=n, when it is G_n^1.
T(2,1) are band groups.
T(3,3) are Shubnikov groups.
For T(n,0) and T(n,n), see [Souvignier, 2006, table 1]. For rows 13, see Litvin.


LINKS

Table of n, a(n) for n=0..10.
H. Grimmer, Comments on tables of magnetic space groups, Acta Cryst., A65 (2009), 145155.
D. B. Litvin, Magnetic Group Tables
B. Souvignier, The fourdimensional magnetic point and space groups, Z. Kristallogr., 221 (2006), 7782.
Index entries for sequences related to groups


EXAMPLE

The triangle begins:
2;
5, 7;
31, 31, 80;
122, 394, 528, 1651;
1202, ...


CROSSREFS

Cf. A293060, A293061, A293062.
Sequence in context: A192560 A174288 A293062 * A215211 A118786 A083777
Adjacent sequences: A293060 A293061 A293062 * A293064 A293065 A293066


KEYWORD

nonn,tabl,hard,more


AUTHOR

Andrey Zabolotskiy, Sep 29 2017


STATUS

approved



